Extensions of Szegö's theory of orthogonal polynomials,III

Let {ø _n (dμ)} be a system of orthonormal polynomials on the unit circle with respect to a measuredμ. Szegö's theory is concerned with the asymptotic behavior ofø _n (dμ) when logμ′∈L ¹. In what follows we will discuss the asymptotic behavior of the ratioø _n (dμ ₂)/ø _n (dμ ₁) on the unit circle whendμ ₁ anddμ ₂ are close in a sense (e.g.,dμ ₂=gdμ ₁, where g≥0 is such thatQ(e ^it )g(t) andQ(e ^it )/g(t) are bounded for a suitable polynomialQ) and μ ₁ ^′ >0 almost everywhere or (a somewhat weaker requirement) lim _n→∞Φ _n (dμ ₁,0)=0 for the monic polynomial Φ _n . The asymptotic behavior of the same fraction outside the unit circle was discussed in an earlier paper.     

A class of interaction-round-a-face models and its equivalence with an ice-type model

A new model (called the Temperley-Lieb interactions model) is introduced, in two-dimensional lattice statistics, on a square lattice . The Temperley-Lieb equivalence of this model to the six-vertex, self-dual Potts, critical hard-hexagons and critical nonintersecting string models is established. A graphical equivalence of this model to the six-vertex model generalizes this equivalence to noncritical cases of the above models. The order parameters of a specialization of this model are studied.     

Donor—acceptor interactions of substituted benzenes with molecular chlorine and carbon disulfide

CNDO molecular orbital calculations have been performed to analyze donor—acceptor interactions between molecular chlorine and benzene, toluene, mesitylene and hexamethylbenzene and the, as yet, unreported chlorine—hexafluorobenzene and carbon disulfide—benzene pairs. The stabilization energy and the dipole moment and its derivative (?p/?R_CICI) calculated for the benzene—chlorine complex are in good agreement with the estimated experimental values. The trends in the experimental stabilization energies and the Cl-Cl vibrational frequencies with increasing methyl substitution appear to be well reproduced by the calculations. The charge transferred from the benzene donor is polarized toward the outer chlorine atom or sulfur atom. For hexafluorobenzene-chlorine the direction of electronic charge polarization is reversed from that of the benzene and methylbenzene complexes. The calculated results are discussed within the framework of Muliiken's simplified resonance theory for complexes.     

Lewis base activation of lewis acids. Addition of silyl ketene acetals to aldehydes

The weak Lewis acid silicon tetrachloride can be activated by catalytic amounts of the chiral bisphosphoramide (R,R)-3 to form a highly reactive, chiral trichlorosilyl cation which is an extremely effective promoter of aldol addition reactions between aldehydes and silyl ketene acetals. The tert-butyldimethylsilyl ketene acetal of methyl acetate adds nearly instantaneously to aromatic and olefinic aldehydes as well as aliphatic aldehydes (albeit more slowly) with excellent enantioselectivity. The homologous tert-butyldimethylsilyl ketene acetal of tert-butyl propanoate adds with nearly exclusive anti diastereoselectivity to a similar range of aldehydes also with excellent enantioselectivity. The origin of the slower reaction rate with aliphatic aldehydes is revealed to be the formation of chlorosilyl ether adducts.     

Reactions of tetrahydro-as-triazine-3(2H)-thiories with α, β-difunctional compounds

The results of allowing tetrahydro-as-triazine-3(2H)-thiones to react with various α,β-diiunctional compounds, such as, α-bromoethyl p-toluenesulfonate, chloroacetaldehyde, α-bromophenylacet-uldehyde, phenaeyl bromide, chloroacetonitrile, α-bromophenylaeelonitrile, and α-cyanobenzyl p-toluenesulfonate are discussed. These condensations give either a 5H-thiazolo[3,2-b]-as-triazine or a 2H-thiazolo[2,3-c]-as-triazine.     

A 13C- and 195Pt-NMR. Study of the Complexes trans-PtCl2 (amine) (CH2CH2)

¹³C- and ¹⁹⁵Pt-NMR. spectra for the complexes trans-PtCl₂(amine)(CH₂?CH₂) have been measured. For amine = (S)-N-methyl-α-methylbenzylamine the two diastereomers present may be distinguished from the values ³J(Pt,C). The ¹⁹⁵Pt-chemical shift is shown to be sensitive to subtle differences stemming from intramolecular non-bonded interactions.     

Homoatomic P --> P coordination: a versatile synthetic approach to polyphosphorus dications

Polyphosphorus dications have been synthesised and comprehensively characterised as diphosphine (dppe, dmpe and dpph) linked Ar2P+ Lewis acids (Ar = C6H5); this application of unique homoatomic coordination chemistry provides important building blocks for extended systems.     

The Raman active internal vibrational modes of potassium nitrate

The Raman active internal vibrational modes of single crystal orthorhombic potassium nitrate have been studied in various polarizations. The full multiplet structure predicted by factor group analysis for the v₂ and v₃ regions has been observed for the first time. The expected site group splitting of the v₄ mode was not observed and can be assumed to be less than 0.5 cm^?1.     

Validity of the Hammond postulate and constraints on general one-dimensional reaction barriers

The Hammond postulate is a useful, qualitative tool that interrelates structural similarities between reactants, transition structures, and products with the exo- or endothermicity of reactions. It applies to most chemical reactions, although several exceptions are known. In this study the following problem is addressed: is it possible to formulate conditions for the validity of the quantitative Hammond postulate in terms of simple physical quantities characteristic to the molecules involved? A detailed analysis is given for the conditions of validity of the postulate, in terms of bounds on the internal forces and force constants of nuclear arrangements encountered along a reaction path. We have determined a broad class of constraints on barrier shapes that must be satisfied in order to obtain a critical situation that violates the Hammond postulate: a reactant-like transition structure (“transition state”) for endothermic reactions, and a product-like one for exothermic reactions. The general constraints are formulated in terms of physically meaningful quantities: (i) energy differences, (ii) restrictions on slopes (e.g., an upper bound on internal forces), and (iii) restrictions on curvatures (e.g., upper bounds on force constants) along potential curves.